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SaniShahbaz

                                         Question # 1

Answer:

It would cost [tex]50x+30[/tex] dollars to put fencing around this garden.

Step-by-step explanation:

In Linda's garden each side is:

  • either [tex]3x-5[/tex] feet or [tex]2x+8[/tex] feet

so

We need to determine the perimeter of the rectangle in order to figure out how much fencing there is.

[tex]P=\left(3x-5\right)+\left(2x+8\right)+\left(3x-5\right)+\left(2x+8\right)[/tex]

As price per foot of fencing is 5  dollars.

So multiply this by  5  dollars.

[tex]5\left(P\right)=5\left[\left(3x-5\right)+\left(2x+8\right)+\left(3x-5\right)+\left(2x+8\right)\right][/tex]

solving

[tex]5\left[\left(3x-5\right)+\left(2x+8\right)+\left(3x-5\right)+\left(2x+8\right)\right][/tex]

[tex]=5\left(\left(3x-5\right)+\left(2x+8\right)+\left(3x-5\right)+\left(2x+8\right)\right)[/tex]

[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]

[tex]=5\left(3x-5+2x+8+3x-5+2x+8\right)...[A][/tex]

[tex]\mathrm{Simplify}\:3x-5+2x+8+3x-5+2x+8[/tex]

[tex]3x-5+2x+8+3x-5+2x+8[/tex]

[tex]=3x+2x+3x+2x-5+8-5+8[/tex]

[tex]=10x-5+8-5+8[/tex]

[tex]=10x+6[/tex]

so Equation [A] becomes

[tex]=5\left(10x+6\right)[/tex]

[tex]=50x+30[/tex]

Therefore, it would cost [tex]50x+30[/tex] dollars to put fencing around this garden.

                                              Question # 2

Answer:

The possible dimensions of the rectangle are  [tex]\left(x-5\right)\left(x+7\right)[/tex].

Step-by-step explanation:

As the rectangle has the area = [tex]x^2+2x-35[/tex]

As

Area = Length × Width

The dimensions of the rectangle could be found by factoring the area:

[tex]x^2+2x-35[/tex]

[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]

[tex]=\left(x^2-5x\right)+\left(7x-35\right)[/tex]

[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2-5x\mathrm{:\quad }x\left(x-5\right)[/tex]

[tex]\mathrm{Factor\:out\:}7\mathrm{\:from\:}7x-35\mathrm{:\quad }7\left(x-5\right)[/tex]

[tex]=x\left(x-5\right)+7\left(x-5\right)[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}x-5[/tex]

[tex]=\left(x-5\right)\left(x+7\right)[/tex]

Therefore, the possible dimensions of the rectangle are  [tex]\left(x-5\right)\left(x+7\right)[/tex].

kudzordzifrancis

Question 1.

The dimensions of the rectangle is given as 3x-5 by 2x+8.

The perimeter of a rectangle is given by:

[tex]P= 2(l + w)[/tex]

We substitute the dimensions to get:

[tex]P= 2(3x - 5 + 2x + 8)[/tex]

We simplify to obtain:

[tex]P= 2(5x + 3)[/tex]

[tex]P= 10x + 6[/tex]

If each foot costs $5 then x feet will cost 5x dollars.

Therefore the total cost of fencing will be;

[tex]10(5x) + 6 \times 5= 50x + 30[/tex]

The total cost in terms of x is 50x+30

Question 2.

The area of the rectangle is given as

[tex] {x}^{2} - 2x - 35[/tex]

We can factor to find the possible dimensions of this rectangle.

We split the middle term to get:

[tex] {x}^{2} + 5x - 7x - 35[/tex]

We factor by grouping:

[tex]x(x +5 ) - 7(x + 5)[/tex]

We factor further to get:

[tex](x - 7)(x + 5)[/tex]

The possible dimensions are x-7 by x+5

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